Schottky Defect - Definition, Examples, Diagram, Formula, Characteristics, FAQs

What Is Schottky Defect?

When an equal number of cations and anions are missing from the lattice, a Schottky defect occurs. Lattice structures (also known as crystals) are far from flawless, just like the human body. Our bodies try hard to make things proportionate, but sometimes our right foot is bigger than our left; similarly, crystals try to organise their ions in a tight arrangement, but sometimes an ion slips to another position or just disappears.

Realistically, it is to be expected that crystals will deviate from their normal sequence (not surprising considering defects occur at temperatures greater than 0 K). There are numerous ways for a crystal to lose its order (and hence develop faults); these defects are classified as Point Defects, Line Defects, and other types of defects.

Visual Representation of Schottky Defect

Schottky Defects in Specific Areas

Point defects in lattice structures (or crystals) can be one of two types:

atoms or ions that have left their original location (thus creating vacancies).

Interstitials are formed by atoms or ions slipping into the small gaps between other atoms or ions; as atoms or ions in crystals occupy interstitials, they intrinsically become (make) interstitials.

Also, students can refer,

• NCERT solutions for Class 12 Chemistry Chapter 1 The Solid State
• NCERT Exemplar Class 12 Chemistry Solutions Chapter 1 The Solid State

Schottky Defect Characteristics

When heat is applied to crystals of ionic substances, Schottky defect forms. Thermal oscillations occur inside the crystal as the temperature rises due to the heat. As a result, gaps appear in the crystal pattern. The availability of ions in chemical compounds causes voids to form.

The "n" ions of X and the "m" ions of Y, for example, will exit the lattice to generate a vacancy in an ionic compound with the formula X_nY_m. A Schottky cluster is a collection of these job openings.

Properties Of The Schottky Defect

Vacancy Formation:

• In a Schottky defect, a cation and an anion are both missing from the crystal lattice at specific sites, creating vacancies.

• The number of cations and anions missing is always equal, maintaining the overall neutrality of the crystal.

Density Decrease:

• The removal of ions from the lattice results in a reduction in the overall density of the crystal. Since there is a loss of matter without a corresponding increase in the crystal’s size, the crystal becomes less dense compared to a perfect crystal.

Electrical Neutrality:

• The Schottky defect ensures electrical neutrality because the number of positive and negative charges removed is the same. This distinguishes it from other defects that might cause an imbalance in charge.

Occurs in High Symmetry Crystals:

• Schottky defects are most commonly found in ionic solids that have a high symmetry and closely packed structures, such as NaCl or KCl.

Low Temperature Formation:

• Schottky defects typically form at high temperatures, as thermal energy is required to overcome the lattice energy and create vacancies.

Impact on Ionic Conductivity:

• Schottky defects can increase the ionic conductivity in the material, as the missing ions create vacancies that can facilitate the movement of ions through the lattice.

Formation Energy:

• The formation of Schottky defects requires a certain amount of energy, known as the vacancy formation energy, which is related to the bond strength between the cations and anions in the lattice.

Non-Stoichiometric:

• Because of the missing ions, Schottky defects result in a non-stoichiometric crystal structure, meaning the actual number of ions may deviate slightly from the ideal stoichiometric ratio in the bulk material.

Schottky Defects Formula

Heat is used to create Schottky defects in solid crystals. The following formula can be used to compute the faults at a given temperature:

N_s×≈N_e -H_s/2RT

Were,

At temperature T, N_s = number of Schottky defects per unit volume (in Kelvins)

H_s is the enthalpy of producing a single flaw.

R is the gas constant.

T stands for absolute temperature (in K)

The following formula can be used to calculate N:

N= (Ionic Crystal Compound Density NA) / (Molar Mass of Ionic Crystal Compound)

Schottky Defect Examples

A Schottky defect is a type of crystal defect that occurs mostly in strongly ionic or highly coordinated substances. The size difference between the anions and the cations in the compound's lattice is quite modest.

Examples of Schottky defect

• Sodium chloride (NaCl)
• potassium chloride (KCl)
• potassium bromide (KBr)
• caesium chloride (CsCl) and silver bromide are some examples of salts with Schottky faults (AgBr).

The following formula can be used to calculate N:

N= (Ionic Crystal Compound Density NA) / (Molar Mass of Ionic Crystal Compound)

Differentiate Between Frenkel and Schottky Defects

Despite the fact that both the Schottky and Frenkel defects are point defects that only arise in ionic compounds, there is a significant distinction between them. The following table lists the differences between the Schottky and Frenkel defects.

Points To Remember About The Schottky Defect

The Schottky defect is a point defect in which both cation and anion are missing in equal amounts from the lattice site. NaCl, CaCl, and other salts are examples.

Walter H. Schottky, a German physicist, discovered the Schottky Defect, often known as the small shot effect.

When heat is applied to crystals of ionic substances, Schottky defects form.

Only ionic substances have the Schottky and Frenkel defects, which are point defects. When both cation and anion depart their lattice positions and generate a pair of Vacancy Defects, the Schottky defect occurs. When an atom (particularly a cation) departs its initial lattice position and occupies an interstitial space, the Frenkel Defect occurs.

Some Solved Examples

Question.1 Which of the following have Schottky defect ?

1) ZnS

2) NaCl

3) CuBr

4) AgCl

Solution:

As we learnt in
$\%$ of missing unit $=\left(\frac{d_{\text {theoretical }}-d_{\text {experimental }}}{d_{\text {theoretical }}}\right) \times 100$
- wherein

This defect is common in the compound having a high coordination number and almost equal size of cation and anion.
ex: $\mathrm{NaCl}, \mathrm{KCl}, {\mathrm{CsCl}}, {\mathrm{AgBr}}$ etc
Crystal with higher coordination numbers are suffering from ${\text { Schottky's defect. } \mathrm{NaCl}}$ has a high coordination number i.e. 6:6.
Hence, the answer is the option (2).

Question.2 Which of the following ionic solids exhibits Frenkel defect?
1) LiF (correct)
2) NaCl
3) CaO
4) KBr

Solution:

The correct answer is option (a)LiF. LiF also known as lithium fluoride, exhibits Frenkel defect. Frenkel defect is a type of point defect in ionic solids where a cation is displaced from its regular lattice site to an interstitial site. LiF is an ionic solid in which cations are small in size and can easily move to an interstitial site, leaving behind a vacancy at its original lattice site. NaCl (sodium chloride), CaO (calcium oxide), and K Br (potassium bromide) do not exhibit Frenkel defect as their cations are larger in size and not as easily movable. Hence, the correct answer is option (a) LiF

Hence, the answer is the option (1).

Question.3 A crystal is doped with $10^{22}$ boron atoms $/ \mathrm{m}^3$. If the intrinsic carrier concentration is $5 \times 10^{16} \mathrm{~m}^{-3}$ at room temperature, what is the excess carrier concentration?
1) (correct) $8.5 \times 10^{12} \mathrm{~m}^{-3}$
2) $2.5 \times 10^7 \mathrm{~m}^{-3}$
3) $5 \times 10^7 \mathrm{~m}^{-3}$
4) $8.5 \times 10^{16} \mathrm{~m}^{-3}$

Solution:

The excess carrier concentration can be calculated as $\left(n_d-n_i\right)=\left(10^{22} \mathrm{~m}^{-3}-5 \times 10^{16} \mathrm{~m}^{-3}\right)=8.5 \times 10^{12} \mathrm{~m}^{-3}$ where $n_d$ is the donor concentration and $n_i$ is the intrinsic carrier concentration.

Hence, the answer is the option (1).

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